ABSTRACT
In this exploration, students connect the Pythagorean theorem to similarity and proportion concepts in order to make new discoveries about square roots and to solve a challenging measurement problem. Before they begin, check that they know the words congruent (≅) and similar (~), and remind them that corresponding vertices belong in the same position of polygons' names. For example, △MTC ~ △AXR means that the triangles are similar, and that M and A, T and X, and C and R respectively are in corresponding positions in the triangles.
